{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "neural-networks-tutorial-2.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOTqSivQr5alWGAkSQpusm8",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/towardsai/tutorials/blob/master/neural_networks_tutorial_part_2/neural_networks_tutorial_2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2cDunYzdhOcI"
      },
      "source": [
        "# Building Neural Networks from Scratch with Python Code and Math in Detail - II\n",
        "\n",
        "* Tutorial: https://towardsai.net/p/machine-learning/building-neural-networks-with-python-code-and-math-in-detail-ii-bbe8accbf3d1\n",
        "\n",
        "* Github: https://github.com/towardsai/tutorials/tree/master/neural_networks_tutorial_part_2"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "867gZ8KJhBwJ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "fa02ee00-07ac-4ba6-938a-93bbfd16db66"
      },
      "source": [
        "# Import required libraries :\n",
        "import numpy as np\n",
        "# Define input features :\n",
        "input_features = np.array([[0,0],[0,1],[1,0],[1,1]])\n",
        "print (input_features.shape)\n",
        "print (input_features)\n",
        "# Define target output :\n",
        "target_output = np.array([[0,1,1,1]])\n",
        "# Reshaping our target output into vector :\n",
        "target_output = target_output.reshape(4,1)\n",
        "print(target_output.shape)\n",
        "print (target_output)\n",
        "# Define weights :\n",
        "# 6 for hidden layer\n",
        "# 3 for output layer\n",
        "# 9 total\n",
        "weight_hidden = np.array([[0.1,0.2,0.3],\n",
        " [0.4,0.5,0.6]])\n",
        "weight_output = np.array([[0.7],[0.8],[0.9]])\n",
        "# Learning Rate :\n",
        "lr = 0.05\n",
        "# Sigmoid function :\n",
        "def sigmoid(x):\n",
        " return 1/(1+np.exp(-x))\n",
        "# Derivative of sigmoid function :\n",
        "def sigmoid_der(x):\n",
        " return sigmoid(x)*(1-sigmoid(x))\n",
        " \n",
        "for epoch in range(200000):\n",
        " # Input for hidden layer :\n",
        " input_hidden = np.dot(input_features, weight_hidden)\n",
        " \n",
        " # Output from hidden layer :\n",
        " output_hidden = sigmoid(input_hidden)\n",
        " \n",
        " # Input for output layer :\n",
        " input_op = np.dot(output_hidden, weight_output)\n",
        " \n",
        " # Output from output layer :\n",
        " output_op = sigmoid(input_op)\n",
        "#==========================================================\n",
        " # Phase1\n",
        " \n",
        " # Calculating Mean Squared Error :\n",
        " error_out = ((1 / 2) * (np.power((output_op - target_output), 2)))\n",
        " print(error_out.sum())\n",
        " \n",
        " # Derivatives for phase 1 :\n",
        " derror_douto = output_op - target_output\n",
        " douto_dino = sigmoid_der(input_op) \n",
        " dino_dwo = output_hidden\n",
        " derror_dwo = np.dot(dino_dwo.T, derror_douto * douto_dino)\n",
        "#===========================================================\n",
        " # Phase 2 \n",
        " # derror_w1 = derror_douth * douth_dinh * dinh_dw1\n",
        " # derror_douth = derror_dino * dino_outh\n",
        " \n",
        " # Derivatives for phase 2 :\n",
        " derror_dino = derror_douto * douto_dino\n",
        " dino_douth = weight_output\n",
        " derror_douth = np.dot(derror_dino , dino_douth.T)\n",
        " douth_dinh = sigmoid_der(input_hidden) \n",
        " dinh_dwh = input_features\n",
        " derror_wh = np.dot(dinh_dwh.T, douth_dinh * derror_douth)\n",
        "# Update Weights\n",
        " weight_hidden -= lr * derror_wh\n",
        " weight_output -= lr * derror_dwo # TODO: Verify update from derror_wo to derror_dwo\n",
        " \n",
        "# Final hidden layer weight values :\n",
        "print (weight_hidden)\n",
        "# Final output layer weight values :\n",
        "print (weight_output)\n",
        "# Predictions :\n",
        "#Taking inputs :\n",
        "single_point = np.array([1,1])\n",
        "#1st step :\n",
        "result1 = np.dot(single_point, weight_hidden) \n",
        "#2nd step :\n",
        "result2 = sigmoid(result1)\n",
        "#3rd step :\n",
        "result3 = np.dot(result2,weight_output)\n",
        "#4th step :\n",
        "result4 = sigmoid(result3)\n",
        "print(result4)\n",
        "#=================================================\n",
        "#Taking inputs :\n",
        "single_point = np.array([0,0])\n",
        "#1st step :\n",
        "result1 = np.dot(single_point, weight_hidden) \n",
        "#2nd step :\n",
        "result2 = sigmoid(result1)\n",
        "#3rd step :\n",
        "result3 = np.dot(result2,weight_output)\n",
        "#4th step :\n",
        "result4 = sigmoid(result3)\n",
        "print(result4)\n",
        "#=====================================================\n",
        "#Taking inputs :\n",
        "single_point = np.array([1,0])\n",
        "#1st step :\n",
        "result1 = np.dot(single_point, weight_hidden) \n",
        "#2nd step :\n",
        "result2 = sigmoid(result1)\n",
        "#3rd step :\n",
        "result3 = np.dot(result2,weight_output)\n",
        "#4th step :\n",
        "result4 = sigmoid(result3)\n",
        "print(result4)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
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            "[[-3.82270773  2.36324803  3.13867107]\n",
            " [-3.79490945  2.45183148  3.18541383]]\n",
            "[[-13.22689481]\n",
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            "[0.99462917]\n",
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            "[0.99071056]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dLelqmJaXNIw",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "ad414498-d800-46e7-f883-805e309f2f2b"
      },
      "source": [
        "# Import required libraries :\n",
        "import numpy as np# Define input features :\n",
        "input_features = np.array([[0,0],[0,1],[1,0],[1,1]])\n",
        "print (input_features.shape)\n",
        "print (input_features)# Define target output :\n",
        "target_output = np.array([[0,1,1,1]])# Reshaping our target output into vector :\n",
        "target_output = target_output.reshape(4,1)\n",
        "print(target_output.shape)\n",
        "print (target_output)# Define weights :\n",
        "weights = np.array([[0.1],[0.2]])\n",
        "print(weights.shape)\n",
        "print (weights)# Define learning rate :\n",
        "lr = 0.05# Sigmoid function :\n",
        "def sigmoid(x):\n",
        "    return 1/(1+np.exp(-x))# Derivative of sigmoid function :\n",
        "def sigmoid_der(x):\n",
        "    return sigmoid(x)*(1-sigmoid(x))# Main logic for neural network :\n",
        "# Running our code 10000 times :for epoch in range(10000):\n",
        "    inputs = input_features#Feedforward input :\n",
        "    pred_in = np.dot(inputs, weights)#Feedforward output :\n",
        "    pred_out = sigmoid(pred_in)#Backpropogation \n",
        "    #Calculating error\n",
        "    error = pred_out - target_output\n",
        "    x = error.sum()\n",
        "    \n",
        "    #Going with the formula :\n",
        "    print(x)\n",
        "    \n",
        "    #Calculating derivative :\n",
        "    dcost_dpred = error\n",
        "    dpred_dz = sigmoid_der(pred_out)\n",
        "    \n",
        "    #Multiplying individual derivatives :\n",
        "    z_delta = dcost_dpred * dpred_dz#Multiplying with the 3rd individual derivative :\n",
        "    inputs = input_features.T\n",
        "    weights -= lr * np.dot(inputs, z_delta)#Predictions :#Taking inputs :\n",
        "single_point = np.array([1,0])\n",
        "#1st step :\n",
        "result1 = np.dot(single_point, weights) \n",
        "#2nd step :\n",
        "result2 = sigmoid(result1)\n",
        "#Print final result\n",
        "print(result2)#====================================\n",
        "#Taking inputs :\n",
        "single_point = np.array([0,0])\n",
        "#1st step :\n",
        "result1 = np.dot(single_point, weights) \n",
        "#2nd step :\n",
        "result2 = sigmoid(result1)\n",
        "#Print final result\n",
        "print(result2)#===================================\n",
        "#Taking inputs :\n",
        "single_point = np.array([1,1])\n",
        "#1st step :\n",
        "result1 = np.dot(single_point, weights) \n",
        "#2nd step :\n",
        "result2 = sigmoid(result1)\n",
        "#Print final result\n",
        "print(result2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(4, 2)\n",
            "[[0 0]\n",
            " [0 1]\n",
            " [1 0]\n",
            " [1 1]]\n",
            "(4, 1)\n",
            "[[0]\n",
            " [1]\n",
            " [1]\n",
            " [1]]\n",
            "(2, 1)\n",
            "[[0.1]\n",
            " [0.2]]\n",
            "[0.52497919]\n",
            "[0.5]\n",
            "[0.57444252]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nmFrl4yudnrB",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "fe8f5b93-fff5-4f6b-8b33-150d95aac81a"
      },
      "source": [
        "# Import required libraries :\n",
        "import numpy as np\n",
        "# Define input features :\n",
        "input_features = np.array([[0,0],[0,1],[1,0],[1,1]])\n",
        "print (input_features.shape)\n",
        "print (input_features)\n",
        "# Define target output :\n",
        "target_output = np.array([[0,1,1,0]])\n",
        "# Reshaping our target output into vector :\n",
        "target_output = target_output.reshape(4,1)\n",
        "print(target_output.shape)\n",
        "print (target_output)\n",
        "# Define weights :\n",
        "# 8 for hidden layer\n",
        "# 4 for output layer\n",
        "# 12 total \n",
        "weight_hidden = np.random.rand(2,4)\n",
        "weight_output = np.random.rand(4,1)\n",
        "# Learning Rate :\n",
        "lr = 0.05\n",
        "# Sigmoid function :\n",
        "def sigmoid(x):\n",
        " return 1/(1+np.exp(-x))\n",
        "# Derivative of sigmoid function :\n",
        "def sigmoid_der(x):\n",
        " return sigmoid(x)*(1-sigmoid(x))\n",
        "# Main logic :\n",
        "for epoch in range(200000):\n",
        " # Input for hidden layer :\n",
        " input_hidden = np.dot(input_features, weight_hidden)\n",
        " \n",
        " # Output from hidden layer :\n",
        " output_hidden = sigmoid(input_hidden)\n",
        " \n",
        " # Input for output layer :\n",
        " input_op = np.dot(output_hidden, weight_output)\n",
        " \n",
        " # Output from output layer :\n",
        " output_op = sigmoid(input_op)\n",
        "#========================================================================\n",
        " # Phase1\n",
        " \n",
        " # Calculating Mean Squared Error :\n",
        " error_out = ((1 / 2) * (np.power((output_op - target_output), 2)))\n",
        " print(error_out.sum())\n",
        " \n",
        " \n",
        " # Derivatives for phase 1 :\n",
        " derror_douto = output_op - target_output\n",
        " douto_dino = sigmoid_der(input_op) \n",
        " dino_dwo = output_hidden\n",
        " derror_dwo = np.dot(dino_dwo.T, derror_douto * douto_dino)\n",
        "# ========================================================================\n",
        " # Phase 2\n",
        "# derror_w1 = derror_douth * douth_dinh * dinh_dw1\n",
        " # derror_douth = derror_dino * dino_outh\n",
        " \n",
        " # Derivatives for phase 2 :\n",
        " derror_dino = derror_douto * douto_dino\n",
        " dino_douth = weight_output\n",
        " derror_douth = np.dot(derror_dino , dino_douth.T)\n",
        " douth_dinh = sigmoid_der(input_hidden) \n",
        " dinh_dwh = input_features\n",
        " derror_dwh = np.dot(dinh_dwh.T, douth_dinh * derror_douth)\n",
        "# Update Weights\n",
        " weight_hidden -= lr * derror_dwh\n",
        " weight_output -= lr * derror_dwo\n",
        " \n",
        " \n",
        "# Final values of weight in hidden layer :\n",
        "print (weight_hidden)\n",
        "# Final values of weight in output layer :\n",
        "print (weight_output)\n",
        "#Taking inputs :\n",
        "single_point = np.array([0,-1])\n",
        "#1st step :\n",
        "result1 = np.dot(single_point, weight_hidden) \n",
        "#2nd step :\n",
        "result2 = sigmoid(result1)\n",
        "#3rd step :\n",
        "result3 = np.dot(result2,weight_output)\n",
        "#4th step :\n",
        "result4 = sigmoid(result3)\n",
        "print(result4)\n",
        "#Taking inputs :\n",
        "single_point = np.array([0,5])\n",
        "#1st step :\n",
        "result1 = np.dot(single_point, weight_hidden) \n",
        "#2nd step :\n",
        "result2 = sigmoid(result1)\n",
        "#3rd step :\n",
        "result3 = np.dot(result2,weight_output)\n",
        "#4th step :\n",
        "result4 = sigmoid(result3)\n",
        "print(result4)\n",
        "#Taking inputs :\n",
        "single_point = np.array([1,1.2])\n",
        "#1st step :\n",
        "result1 = np.dot(single_point, weight_hidden) \n",
        "#2nd step :\n",
        "result2 = sigmoid(result1)\n",
        "#3rd step :\n",
        "result3 = np.dot(result2,weight_output)\n",
        "#4th step :\n",
        "result4 = sigmoid(result3)\n",
        "print(result4)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
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}